Measurement of the $2S_{1/2},F$=$0 \rightarrow 2P_{1/2},F$=$1$ transition in Muonium

Abstract

Muons are puzzling physicists since their discovery when they were first thought to be the meson predicted by Yukawa to mediate the strong force. The recent results at Fermilab on the muon g-2 anomaly puts the muonic sector once more under the spotlight and calls for new measurements with this fascinating particle. Here we present the results of the first measurement of the $2S_{1/2},F$=$0 \rightarrow 2P_{1/2},F$=$1$ transition in Muonium, the hydrogen-like bound state of a positive muon and an electron. The measured value of 580.6 $\pm$6.8 MHz is in agreement with the theoretical calculations. From this measurement a value of the Lamb shift of 1045.5 $\pm$6.8 MHz is extracted, compatible with previous experiments. We also determine for the first time the $2S$ hyperfine splitting in Muonium to be 559.6$\pm$7.2 MHz. The measured transition being isolated from the other hyperfine levels holds the promise to provide an improved determination of the Muonium Lamb shift at a level where bound state QED recoil corrections not accessible in hydrogen could be tested. Such a measurement will also be sensitive to new physics in the muonic sector, e.g. to new bosons which might provide an explanation of the g-2 muon anomaly or Lorentz and CPT violation. We also present the first observation of Muonium in the $n = 3$ excited state opening up the possibility of new precise microwave measurements as realized in hydrogen.